Periods are a class of complex numbers obtained by integrating algebraic differential forms over algebraically-defined domains. From the modern point of view, they appear as coefficients of the comparison isomorphism between de Rham and Betti cohomology of varieties over number fields. This is how motives enter the game.
The aim of this summer school is to introduce students to the applications of different categories of motives to concrete questions on periods. The possibility of giving non-conjectural constructions of the motivic Galois group has opened the way to major new results: a proof of Hoffman's conjecture on multiple zeta values by Francis Brown, and a proof of a geometric analogue of the Kontsevich-Zagier conjecture by Joseph Ayoub.
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Giuseppe Ancona (IRMA Strasbourg), Javier Fresán (ETH Zürich), Simon Pepin Lehalleur (FU Berlin)